Chairman and CEO Ellen Kullman said on CNBC this morning that she hadn’t had any talks with Peltz, of Trian Fund Management, but that she had “heard the rumors” of his position.

Still, that’s not stopping the chemicals and agricultural giant from acting like it has an activist in its midst. DuPont announced amid its second-quarter results that it was looking at “strategic alternatives” for its performance chemicals segment.

In a release the company said the segment generated total sales of $7.2 billion last year, which would have been more than 20% of the company’s total revenue that year.

The segment is DuPont’s second largest by revenue to the key agriculture unit, which brought in more than $10.4 billion in revenue last year.

By adjusted operating profit, performance chemicals only slightly trailed agriculture for 2012, bringing in $1.59 billion, just over half of the total profit for DuPont last year.

The unit includes two businesses — titanium technologies and chemicals & fluoroproducts — which DuPont said could be separated themselves. Among the possible transactions are a spin-off and a sale.

BGC analyst Mark Gulley estimated the business could be worth $8.9 billion.

“As we discussed at our Investors Day in May, we have been carefully weighing the strong cash generation of our Performance Chemicals businesses against their cyclicality and lower growth profile, as well as where the power of DuPont’s integrated science can be differentiated, ” said Kullman in a statement. “We are evaluating options for our Performance Chemicals businesses as part of our ongoing plan to deliver higher growth and greater value creation for our shareholders.”

DuPont shares are up 4.7% to $59.86. The stock is up 9% this month and is trading at a 13-year high.